Chapter 7: The Influence of Teachers on Opportunities to Learn
Summary: Many school reforms have put emphasis on the need for "highly qualified" teachers, such as NCLB; but the definition of a highly qualified mathematics teacher has never been defined. Because of this, there is no common standards for the types of mathematical knowledge required among U.S. primary teacher preparation programs, according to data from TEDs studies, and thus there is a substantial variation in the amount and type of coursework required by these programs. Only about one-third of teacher preparation was in mathematical content for primary school teachers. For secondary mathematics teachers, the general consensus is that they should have more extensive and more in depth mathematical knowledge than primary school teachers. While high school teacher preparation typically requires a major in mathematics, it is simply a desire for middle school teachers to have a major in their field. Despite this hope, however, this chapter explains that teachers typically do not have sufficient knowledge for teaching mathematics and thus do not feel prepared to teach many of the topics that they are required to.
Schmidt & McKnight (2012) defined a qualified teaching force with a 75% criterion, saying that 75% of teachers should feel well prepared to teach a given topic. However, using this criterion, a mere two mathematics topics (the meaning of whole numbers and operations with whole numbers) met this criterion. If the criterion was lowered to 50%, only eight more topics met this standard. For most topics, the median percent of teachers who felt well-prepared was below 50%. The other troubling statistic is the variation across districts. For example, one district had only 25% of its primary school teacher feeling well-prepared to teach geometry while another district had 90%. This variation across districts is similar to middle school teachers due to the strong national movement to include algebra topics in middle school. In one district, no teacher felt prepared to teach linear equations and inequalities while another school had all of its teachers feeling well prepared to teach it. This variation absolutely adds to the inequality of OTL (opportunities to learn) that students face in different schools and districts. The percent of high school topics that teachers felt well-prepared to teach was higher than elementary and middle school teachers because of the fact that high school teachers have greater preparation in content knowledge. Thus, 60% of the topics that high school teachers taught did meet the 75% criterion. However, this is still rather low, and there still was a great variation across districts, especially for geometry.
The reason elementary and middle school teachers feel ill-prepared, according to Schmidt & McKnight (2012), is because they are ill-prepared. Less than 10% of first to fourth grade teachers have a major or minor in mathematics. What is more troubling is in the higher grades; in 7th and 8th grade, this percentage increases to 35% to 40%. Although we would hope that all high school teachers have some degree in mathematics, almost one-third of teachers did not have a major or minor in mathematics; and almost 50% of 9th and 10th grade teachers had no specialization in math. So while it is tempting to blame teachers for our students lack of achievement, clearly the state and districts are also to blame for the lack of requirements of teachers.
Reaction:
I personally found this chapter extremely troubling. Not only is it hard to imagine how little education most teachers have in mathematics, but it's even harder to believe that teachers know that they don't know enough to teach the subject. In my opinion, if a teacher does not feel prepared to teach a certain topic, s/he should not be allowed to teach that topic. Because math is a hierarchical subject, if primary school teachers teach their students topics incorrectly, it will severely hurt them when they are trying to learn more advanced concepts later on. I think that before teachers are allowed to teach any given subject, they must feel confident in all of the topics that they are required to cover in that course. The variation between qualified teachers across school districts and even schools is also very bothersome. The fact that some areas only have a quarter of its teachers feeling prepared to teach certain subjects while others have 90% of teachers feeling prepared is remarkable. It's no wonder that students have such unequal opportunities to learn and that some schools have much higher test scores than others. Schools that have highly qualified teachers obviously will have better test scores, but I had no idea that the variation was to this degree.
Chapter 8: The Role of Textbooks and Tests
Summary: The impact of textbooks on students' opportunities to learn is often overlooked. Textbooks fall somewhere in between the intended curriculum and the implemented curriculum. They act as a bridge between intentions and implementation. Since teachers often do not have time to decide how to present a topic or in what sequence to teach the required topics, textbooks act as a guide to make those decisions. Schmidt & McKnight (2012) describe three different roles that textbooks can play in school. The first case is when textbooks act as the curriculum; they are simply followed page by page to however far the teacher can get by the end of the year. The second case is when a textbook is used only as a supplement to other materials that the teacher decides to use. The more frequent scenario is the third case, that the textbook is a combination of case one and case two, and plays the primary role among several other sources.
Schmidt & McKnight (2012) examined the difference between mathematics textbooks, and their impact on opportunities to learn. They divided all math topics into eight different categories, and then examined the coverage of each topic in different texts. The median coverage of topics in textbooks ranged from 33% to 74%, meaning between one-third and three-fourths of textbooks covered the typical topic for that textbook type. Some of these statistics were extremely shocking; for example, 17% of Algebra I textbooks did not cover the idea of slope. In the general mathematics textbooks, 56% of the books only covered two of the five algebra topics and only 10% covered four of five of them. To have books exclude such essential concepts to the main topic they are supposed to cover absolutely affects students' opportunities to learn, especially if teachers are using the textbook as described in case one.
Two other factors that influence the quality of learning opportunities were also discussed in this chapter: the number of pages in a given textbook and the percent of the book spent on particular topics, and content flow. Based on these two factors, Schmidt & McKnight concluded that U.S. textbooks "appear to offer the worst of all worlds" (180). U.S. textbooks are much longer compared to other countries. An average international 8th grade textbook was 225 pages compared to the average U.S. textbook of 800 pages. One affect of this is that not all topics can be covered when books are this long. More time is spent on earlier topics, and the end of the textbook is never reached. The content flow of U.S. textbooks are also significantly worse than other countries. On average, TIMSS countries' textbooks had approximately 50 breaks in content flow. The three leading U.S. textbooks ranged from around 60 breaks in 12th grade textbooks to over 300 breaks in 4th grade texts.
The final topic covered in this chapter was assessments and tests. Schmidt & McKnight (2012) describe a "chicken and egg paradox" when it comes to tests. The "egg" role is that where tests are "thought of as a way to measure student attainments that result from the learning opportunities students have had" (180). This is compared to the "chicken" role in which tests can influence what content will be covered in the future because past tests can shape future opportunities (though the operative word is "can"). Schmidt & McKnight (2012) then discuss three assessments: state assessments, standardized tests, and high school exit exams. State assessments tend to drive teachers to "teach to the test", while standardized tests allow for schools to be compared against a national sample. Finally, the fact that many states now require a high school exit exam that determines whether or not students receive their diploma was discussed.
Reaction:
I was very interested to learn about the difference in textbooks between the U.S. and other countries. It is something that I never would have thought about otherwise. The points that Schmidt and McKnight bring up are extremely valid though. I don't think I've had a class in which we actually covered the entire textbook, but it was always something that I just never thought happened. It never occurred to me that it meant that we should have shorter textbooks! I would be extremely curious to see what another country's textbook looks like as well. The number of breaks in U.S. textbooks seems awfully high; however I have nothing to compare it to, so I wouldn't know what a textbook with more "flow" was like. I would have liked Schmidt and McKnight to have gone into a little more detail about the impact of assessments, but perhaps they did in another section of the book that I didn't get to read. This is an area that I will do more research about on my own and try to gather additional sources about.
a. Citation for book (In APA style)
Schmidt, W. H., & McKnicght, C. C. (2012). Inequality for all: the challenge of unequal opportunity in American schools. New York: Teachers College Press.
b. Summary of book's argument taken as best you can from the introduction.
Schmidt and McKnight are arguing that school is a game of chance on an unlevel playing field (Schmidt, 2012). They feel as though students not only have unequal opportunities between school distracts, but even between classrooms, specifically in regards to math and science. In the introduction, it is explained that even students who would be expected to do equally as well based on background, upbringing, and general ability do not receive equal opportunities to learn math. They believe that while teachers, administrators, and politicians have the best interest in mind for our students, for example, by implementing the NCLB, the equal opportunities that we try to give our students aren't happening. The chapters in this book are designed to examine the different aspects of schooling and their affect on students' opportunity to learn (OLT) from the differences in curricula between and within states to the teacher's knowledge base and materials used.
c. Brief description of author's background.
William H, Schmidt has a bachelor's degree in mathematics and a PhD in psychometrics and applied statistics. He has served as national research coordinator and executive director of the U.S. National Center, which oversaw the U.S. participation in the Third International Mathematics and Science Study (TIMSS). He has published in several educational journals and has co-authored eight books. He is currently the co-director of the Education Policy Center, co-director of the U.S.-China Center for Research, and director of the NSF PROM/SE project. His present writing and research are focused on concerns about academic content in K-12 schooling, assessment theory, the effects of curriculum on academic achievement, and educational policy regarding mathematics and science (Schmidt, 2012).
Curtis C. McKnight is a professor of mathematics at the University of Oklahoma. He has served as national research coordinator and executive director of the U.S. National Center for the Second International Mathematics Study (SIMS). He has been the senior mathematics consultant to the U.S. Research Center for TIMSS. Some of his areas of focus are cross-national comparative studies, cognitive studies of mathematics learning and performance, and curriculum policy studies (Schmidt, 2012).
d. Description of the scope your reading, e.g. what chapters, (with titles) you plan to read. How was your decision about what to read influenced by your goals concerning the book?
My main interest is in Part II of this book: "Factors that Shape Content Coverage and Increase Inequality". Because of my past experiences with classroom observation, I'm extremely curious about Schmidt and McKnight's point of view on what teachers are required to know and the effect that materials and textbooks have on our students opportunity to learn math. This section covers the following topics:
Chapter 7: The Influence of Teachers on Opportunities to Learn
The Mathematics Content Knowledge that Teachers Should Have
What Teachers Tell Us About Their Knowledge of Mathematics
Why Teachers Feel So Poorly Prepared
The Effects of Teachers' Mathematics Knowledge on Opportunities to Learn
Chapter 8: The Role of Textbooks and Tests
Textbooks: The Potentially Implemented Curriculum
Mathematics Textbooks
Textbook Factors that Influence the Quality of Learning Opportunities
Assessments and Tests
A Last Thought on the Influence of Textbooks and Tests
While Part II is my main interest, Part I will give me a significant amount of background information in regards to content variation between schools, what is being taught and what should be taught in different grades and math classes. Part I also includes information about the affects of tracking in school, which I will read if time permits. The topics in Part I that I will read are:
Chapter 2: One Indivisible Nation?
The Movement Toward Common Standards
The Clash of Two Great Traditions
The Consequences of Local Control of the Curriculum
Content Variation in State Standards
Content Variation Across Local Districts
The Consequences of State and Local Control of the Curriculum
Chapter 3: Social Class, Race, and Equality of Opportunity
Variability in Learning Opportunities Related to SES
Content Opportunities in Urban Districts
Inequality in 8th-Grade Mathematics Among Districts
Expectations Versus Implementation
Chapter 4: Into the Classroom: The Content Opportunities Children Actually Experience
Content Coverage in Elementary Classrooms
Content Coverage in Middle School Classrooms
Social Class Differences in Learning Opportunities
Content Coverage in High School Classrooms
Classroom Variation
e. How do you see the knowledge gained from your portion of the book contributing to the class's understanding of schools, teaching, and/or school reform
I think taking a look into the differences between curricula from different districts along with the drastic differences in what teachers should know and actually know will be very eye-opening to our class. I also think it's important to explore the impact that classroom materials can have on the opportunities our students have to learn. To see the statistics on the variation between what is taught in the classroom from state to state, or even classroom to classroom, will be informative in regards to the idea of a common core curriculum. It will be beneficial for us to see what teachers are actually teaching and how close to (or far from) the curriculum most teachers are. Chapter 3 will also connect well with our reading of Kozol because we will see how the OLT are different because of race and being in an urban school.
Adopt-a-Book Project
Chapter 7: The Influence of Teachers on Opportunities to Learn
Summary:
Many school reforms have put emphasis on the need for "highly qualified" teachers, such as NCLB; but the definition of a highly qualified mathematics teacher has never been defined. Because of this, there is no common standards for the types of mathematical knowledge required among U.S. primary teacher preparation programs, according to data from TEDs studies, and thus there is a substantial variation in the amount and type of coursework required by these programs. Only about one-third of teacher preparation was in mathematical content for primary school teachers. For secondary mathematics teachers, the general consensus is that they should have more extensive and more in depth mathematical knowledge than primary school teachers. While high school teacher preparation typically requires a major in mathematics, it is simply a desire for middle school teachers to have a major in their field. Despite this hope, however, this chapter explains that teachers typically do not have sufficient knowledge for teaching mathematics and thus do not feel prepared to teach many of the topics that they are required to.
Schmidt & McKnight (2012) defined a qualified teaching force with a 75% criterion, saying that 75% of teachers should feel well prepared to teach a given topic. However, using this criterion, a mere two mathematics topics (the meaning of whole numbers and operations with whole numbers) met this criterion. If the criterion was lowered to 50%, only eight more topics met this standard. For most topics, the median percent of teachers who felt well-prepared was below 50%. The other troubling statistic is the variation across districts. For example, one district had only 25% of its primary school teacher feeling well-prepared to teach geometry while another district had 90%. This variation across districts is similar to middle school teachers due to the strong national movement to include algebra topics in middle school. In one district, no teacher felt prepared to teach linear equations and inequalities while another school had all of its teachers feeling well prepared to teach it. This variation absolutely adds to the inequality of OTL (opportunities to learn) that students face in different schools and districts. The percent of high school topics that teachers felt well-prepared to teach was higher than elementary and middle school teachers because of the fact that high school teachers have greater preparation in content knowledge. Thus, 60% of the topics that high school teachers taught did meet the 75% criterion. However, this is still rather low, and there still was a great variation across districts, especially for geometry.
The reason elementary and middle school teachers feel ill-prepared, according to Schmidt & McKnight (2012), is because they are ill-prepared. Less than 10% of first to fourth grade teachers have a major or minor in mathematics. What is more troubling is in the higher grades; in 7th and 8th grade, this percentage increases to 35% to 40%. Although we would hope that all high school teachers have some degree in mathematics, almost one-third of teachers did not have a major or minor in mathematics; and almost 50% of 9th and 10th grade teachers had no specialization in math. So while it is tempting to blame teachers for our students lack of achievement, clearly the state and districts are also to blame for the lack of requirements of teachers.
Reaction:
I personally found this chapter extremely troubling. Not only is it hard to imagine how little education most teachers have in mathematics, but it's even harder to believe that teachers know that they don't know enough to teach the subject. In my opinion, if a teacher does not feel prepared to teach a certain topic, s/he should not be allowed to teach that topic. Because math is a hierarchical subject, if primary school teachers teach their students topics incorrectly, it will severely hurt them when they are trying to learn more advanced concepts later on. I think that before teachers are allowed to teach any given subject, they must feel confident in all of the topics that they are required to cover in that course. The variation between qualified teachers across school districts and even schools is also very bothersome. The fact that some areas only have a quarter of its teachers feeling prepared to teach certain subjects while others have 90% of teachers feeling prepared is remarkable. It's no wonder that students have such unequal opportunities to learn and that some schools have much higher test scores than others. Schools that have highly qualified teachers obviously will have better test scores, but I had no idea that the variation was to this degree.
Chapter 8: The Role of Textbooks and Tests
Summary:
The impact of textbooks on students' opportunities to learn is often overlooked. Textbooks fall somewhere in between the intended curriculum and the implemented curriculum. They act as a bridge between intentions and implementation. Since teachers often do not have time to decide how to present a topic or in what sequence to teach the required topics, textbooks act as a guide to make those decisions. Schmidt & McKnight (2012) describe three different roles that textbooks can play in school. The first case is when textbooks act as the curriculum; they are simply followed page by page to however far the teacher can get by the end of the year. The second case is when a textbook is used only as a supplement to other materials that the teacher decides to use. The more frequent scenario is the third case, that the textbook is a combination of case one and case two, and plays the primary role among several other sources.
Schmidt & McKnight (2012) examined the difference between mathematics textbooks, and their impact on opportunities to learn. They divided all math topics into eight different categories, and then examined the coverage of each topic in different texts. The median coverage of topics in textbooks ranged from 33% to 74%, meaning between one-third and three-fourths of textbooks covered the typical topic for that textbook type. Some of these statistics were extremely shocking; for example, 17% of Algebra I textbooks did not cover the idea of slope. In the general mathematics textbooks, 56% of the books only covered two of the five algebra topics and only 10% covered four of five of them. To have books exclude such essential concepts to the main topic they are supposed to cover absolutely affects students' opportunities to learn, especially if teachers are using the textbook as described in case one.
Two other factors that influence the quality of learning opportunities were also discussed in this chapter: the number of pages in a given textbook and the percent of the book spent on particular topics, and content flow. Based on these two factors, Schmidt & McKnight concluded that U.S. textbooks "appear to offer the worst of all worlds" (180). U.S. textbooks are much longer compared to other countries. An average international 8th grade textbook was 225 pages compared to the average U.S. textbook of 800 pages. One affect of this is that not all topics can be covered when books are this long. More time is spent on earlier topics, and the end of the textbook is never reached. The content flow of U.S. textbooks are also significantly worse than other countries. On average, TIMSS countries' textbooks had approximately 50 breaks in content flow. The three leading U.S. textbooks ranged from around 60 breaks in 12th grade textbooks to over 300 breaks in 4th grade texts.
The final topic covered in this chapter was assessments and tests. Schmidt & McKnight (2012) describe a "chicken and egg paradox" when it comes to tests. The "egg" role is that where tests are "thought of as a way to measure student attainments that result from the learning opportunities students have had" (180). This is compared to the "chicken" role in which tests can influence what content will be covered in the future because past tests can shape future opportunities (though the operative word is "can"). Schmidt & McKnight (2012) then discuss three assessments: state assessments, standardized tests, and high school exit exams. State assessments tend to drive teachers to "teach to the test", while standardized tests allow for schools to be compared against a national sample. Finally, the fact that many states now require a high school exit exam that determines whether or not students receive their diploma was discussed.
Reaction:
I was very interested to learn about the difference in textbooks between the U.S. and other countries. It is something that I never would have thought about otherwise. The points that Schmidt and McKnight bring up are extremely valid though. I don't think I've had a class in which we actually covered the entire textbook, but it was always something that I just never thought happened. It never occurred to me that it meant that we should have shorter textbooks! I would be extremely curious to see what another country's textbook looks like as well. The number of breaks in U.S. textbooks seems awfully high; however I have nothing to compare it to, so I wouldn't know what a textbook with more "flow" was like. I would have liked Schmidt and McKnight to have gone into a little more detail about the impact of assessments, but perhaps they did in another section of the book that I didn't get to read. This is an area that I will do more research about on my own and try to gather additional sources about.
a. Citation for book (In APA style)
Schmidt, W. H., & McKnicght, C. C. (2012). Inequality for all: the challenge of unequal opportunity in American schools. New York: Teachers College Press.
b. Summary of book's argument taken as best you can from the introduction.
Schmidt and McKnight are arguing that school is a game of chance on an unlevel playing field (Schmidt, 2012). They feel as though students not only have unequal opportunities between school distracts, but even between classrooms, specifically in regards to math and science. In the introduction, it is explained that even students who would be expected to do equally as well based on background, upbringing, and general ability do not receive equal opportunities to learn math. They believe that while teachers, administrators, and politicians have the best interest in mind for our students, for example, by implementing the NCLB, the equal opportunities that we try to give our students aren't happening. The chapters in this book are designed to examine the different aspects of schooling and their affect on students' opportunity to learn (OLT) from the differences in curricula between and within states to the teacher's knowledge base and materials used.
c. Brief description of author's background.
William H, Schmidt has a bachelor's degree in mathematics and a PhD in psychometrics and applied statistics. He has served as national research coordinator and executive director of the U.S. National Center, which oversaw the U.S. participation in the Third International Mathematics and Science Study (TIMSS). He has published in several educational journals and has co-authored eight books. He is currently the co-director of the Education Policy Center, co-director of the U.S.-China Center for Research, and director of the NSF PROM/SE project. His present writing and research are focused on concerns about academic content in K-12 schooling, assessment theory, the effects of curriculum on academic achievement, and educational policy regarding mathematics and science (Schmidt, 2012).
Curtis C. McKnight is a professor of mathematics at the University of Oklahoma. He has served as national research coordinator and executive director of the U.S. National Center for the Second International Mathematics Study (SIMS). He has been the senior mathematics consultant to the U.S. Research Center for TIMSS. Some of his areas of focus are cross-national comparative studies, cognitive studies of mathematics learning and performance, and curriculum policy studies (Schmidt, 2012).
d. Description of the scope your reading, e.g. what chapters, (with titles) you plan to read. How was your decision about what to read influenced by your goals concerning the book?
My main interest is in Part II of this book: "Factors that Shape Content Coverage and Increase Inequality". Because of my past experiences with classroom observation, I'm extremely curious about Schmidt and McKnight's point of view on what teachers are required to know and the effect that materials and textbooks have on our students opportunity to learn math. This section covers the following topics:
Chapter 7: The Influence of Teachers on Opportunities to Learn
Chapter 8: The Role of Textbooks and Tests
While Part II is my main interest, Part I will give me a significant amount of background information in regards to content variation between schools, what is being taught and what should be taught in different grades and math classes. Part I also includes information about the affects of tracking in school, which I will read if time permits. The topics in Part I that I will read are:
Chapter 2: One Indivisible Nation?
Chapter 3: Social Class, Race, and Equality of Opportunity
Chapter 4: Into the Classroom: The Content Opportunities Children Actually Experience
e. How do you see the knowledge gained from your portion of the book contributing to the class's understanding of schools, teaching, and/or school reform
I think taking a look into the differences between curricula from different districts along with the drastic differences in what teachers should know and actually know will be very eye-opening to our class. I also think it's important to explore the impact that classroom materials can have on the opportunities our students have to learn. To see the statistics on the variation between what is taught in the classroom from state to state, or even classroom to classroom, will be informative in regards to the idea of a common core curriculum. It will be beneficial for us to see what teachers are actually teaching and how close to (or far from) the curriculum most teachers are. Chapter 3 will also connect well with our reading of Kozol because we will see how the OLT are different because of race and being in an urban school.